The computational content of atomic polymorphism

Author:

Ferreira Gilda1,Vasconcelos Vasco T2

Affiliation:

1. Universidade Aberta, Rua Braamcamp, 90, Lisboa, Portugal

2. LaSIGE, Departamento de Informática, Faculdade de Ciências da Universidade de Lisboa Campo Grande, Ed. C6, Lisboa, Portugal

Abstract

AbstractWe show that the number-theoretic functions definable in the atomic polymorphic system (${\mathbf{F}}_{\mathbf{at}}$) are exactly the extended polynomials. Two proofs of the above result are presented: one, reducing the functions’ definability problem in ${\mathbf{F}}_{\mathbf{at}}$ to definability in the simply typed lambda calculus ($\lambda ^{\rightarrow }$) and the other, directly adapting Helmut Schwichtenberg’s strategy for definability in $\lambda ^{\rightarrow }$ to the atomic polymorphic setting. The uniformity granted in the polymorphic system, when compared with the simply typed lambda calculus, is emphasized.

Funder

Fundação para a Ciência e a Tecnologia

Centro de Matemática e Aplicações da Universidade da Beira Interior

Publisher

Oxford University Press (OUP)

Subject

Logic

Reference16 articles.

1. An elementary fragment of second-order lambda-calculus;Aehlig,2004

2. Comments on predicative logic;Ferreira;Journal of Philosophical Logic,2006

3. Atomic polymorphism;Ferreira;The Journal of Symbolic Logic,2013

4. The faithfulness of ${\mathbf{F}}_{\mathbf{at}}$: a proof-theoretic proof;Ferreira,2015

5. An elementary proof of strong normalization for atomic $\mathbf{F}$;Ferreira;Bulletin of the Section of Logic,2016

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Type inhabitation of atomic polymorphism is undecidable;Journal of Logic and Computation;2021-01-12

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